Cognitive Foundations of Probability

34 Pages Posted: 14 Jan 2002  

Itzhak Gilboa

Tel Aviv University - Eitan Berglas School of Economics; HEC Paris - Economics & Decision Sciences

David Schmeidler

Tel Aviv University

Date Written: December 2001

Abstract

Prediction is based on past cases. We assume that a predictor can rank eventualities according to their plausibility given any memory that consists of repetitions of past cases. In a companion paper, we show that under mild consistency requirements, these rankings can be represented by numerical functions, such that the function corresponding to each eventuality is linear in the number of case repetitions. In this paper we extend the analysis to rankings of events. Our main result is that a cancellation condition a la de Finetti implies that these functions are additive with respect to union of disjoint sets. If the set of past cases coincides with the set of possible eventualities, natural conditions are equivalent to ranking events by their empirical frequencies. More generally, our results may describe how individuals form probabilistic beliefs given cases that are only partially pertinent to the prediction problem at hand, and how this subjective measure of pertinence can be derived from likelihood rankings.

Keywords: Bayesian Prior, Case-based Decision Theory, Qualitative Probabilities

JEL Classification: D80

Suggested Citation

Gilboa, Itzhak and Schmeidler, David, Cognitive Foundations of Probability (December 2001). Cowles Foundation Discussion Paper No. 1340. Available at SSRN: https://ssrn.com/abstract=295725

Itzhak Gilboa (Contact Author)

Tel Aviv University - Eitan Berglas School of Economics ( email )

P.O. Box 39040
Ramat Aviv, Tel Aviv, 69978
Israel
972-3-640-6423 (Phone)
972-3-640-9908 (Fax)

HEC Paris - Economics & Decision Sciences

Paris
France

David Schmeidler

Tel Aviv University ( email )

P.O. Box 39040
Ramat Aviv, Tel Aviv, 69978
Israel
+972-3-640-9643 (Phone)
+972-3-640-9357 (Fax)

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